Subgroups — #16864643

Order 4336.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₄₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₀₈₄	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₇₁	—	2	1	no	—
5	C₄×C₂₇₁	C₂²	1	1	yes	characteristic
6	Dic₂₇₁	—	2	1	no	—
7	C₂×C₂₇₁	D₄	1	1	yes	characteristic
8	D₂₇₁	—	4	1	no	—
9	C₂₇₁	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	SD₁₆	—	271	1	no	maximal, Sylow
11	Q₈	—	271	1	no	—
12	D₄	—	271	1	no	—
13	C₈	D₂₇₁	1	1	yes	characteristic, complemented
14	C₂²	—	542	1	no	—
15	C₄	—	542	1	no	—
16	C₄	C₂×D₂₇₁	1	1	yes	characteristic
17	C₂	—	1084	1	no	—
18	C₂	D₁₀₈₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.